Recent Developments on Reaction Automata Theory: A Survey

Part of the Mathematics for Industry book series (MFI, volume 9)


This paper surveys recent developments on the theory of reaction automata, which has been lately initiated in [17] to model and analyze in the computational framework the behaviors of biochemical reactions in nature. Reaction automata (RAs) have been proposed as computing models for accepting string languages. RAs may be taken as a kind of an extension of reaction systems in that they deal with multisets rather than (usual) sets being dealt with in reaction systems. A computation process by an RA is performed in such a way that after taking in the system an input symbol from the environment, the RA changes its state (represented by a multiset) by applying reaction rules to the multiset in the manner designated, where the maximally parallel manner is considered as well as the (usual) sequential manner. An input sequence of symbols is accepted if the RA stays in a final state (i.e., a designated multiset) at some moment after reading through the input. Thus, RAs may also be regarded as a variant of finite automata in which multisets are used to play a role of (unbounded number of) states. The presented results are all from [16, 17, 18] and include: RAs have the Turing universal computation power, the computation power of exponential-bounded RAs coincides with that of the linear-bounded Turing machines, the computation power of linear-bounded RAs is incomparable to that of pushdown automata. Further, the case for RAs with sequential mode of rule applications is also investigated.


Models of biochemical reactions Reaction automata Multisets Chomsky hierarchy Turing computability 



The work of F. Okubo was in part supported by Grants-in-Aid for Young Scientists (B) No.24700304, Japan Society for the Promotion of Science. The work of T.Yokomori was in part supported by a Waseda University Grant for Special Research Projects: 2012B-050 and 2013B-063, and also by a Grant-in-Aid for Scientific Research on Innovative Areas "Molecular Robotics" (No.24104003) of the Ministry of Education, Culture, Sports, Science, and Technology, Japan.


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© Springer Japan 2015

Authors and Affiliations

  1. 1.Faculty of Arts and ScienceKyushu UniversityNishi-kuJapan
  2. 2.Faculty of Education and Integrated Arts and SciencesWaseda UniversityShinjuku-KuJapan

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